Picture the part of your body that makes up your neck. Are you picturing it? That's a building block that makes up your body. A really important one. If you didn't have that neck, you wouldn't look like a person at all. Sound familiar? It should! Because that part of your neck is a radical! Just like part of your neck is a building block of your body, the radical is a building block of kanji. Get it? I sure hope so!
This is a jukugo word that uses the on'yomi readings of the kanji. You haven't learned this reading for 首 yet, so here's a mnemonic to help you:
When you need a radical to make a new kanji, you just press a button and the radical comes tumbling down the radical chute (しゅ). There's definitely no rhyme or reason to radical picking, it's just whatever pops out of the ol' chute.
to look up a radical
to teach radicals
to learn radicals
What is the radical of this character?
There are many radical names.
The radical for the kanji for "cut" is "sword."